Edge Detection Phil Mlsna, Ph.D. Dept. of Electrical Engineering Northern Arizona University

Some Important Topics in Image Processing Contrast enhancement Filtering (both spatial and frequency domains) Restoration Segmentation Image Compression etc. EE 460/560 course, Fall 2003 (formerly CSE 432/532) Edge Detection uses spatial filtering to extract important information from a scene.

Types of Edges Physical Edges Image Edges Different objects in physical contact Spatial change in material properties Abrupt change in surface orientation Image Edges In general: Boundary between contrasting regions in image Specifically: Abrupt local change in brightness Image edges are important clues for identifying and interpreting physical edges in the scene.

Goal: Produce an Edge Map Original Image Edge Map

Edge Detection Concepts in 1-D Edges can be characterized as either: local extrema of zero-crossings of

Continuous Gradient But is a vector. We really need a scalar that gives a measure of edge “strength.” This is the gradient magnitude. It’s isotropic.

Classification of Points Let points that satisfy be edge points. PROBLEM: T Non-zero edge width Stronger gradient magnitudes produce thicker edges. To precisely locate the edge, we need to thin. Ideally, edges should be only one point thick.

Practical Gradient Algorithm Compute for all points. Threshold to produce candidate edge points. Thin by testing whether each candidate edge point is a local maximum of along the direction of . Local maxima are classified as edge points.

Cameraman image Thresholded Gradient Thresholded and Thinned

Directional Edge Detection Horizontal operator (finds vertical edges) Vertical operator (finds horizontal edges) finds edges perpendicular to the direction

Horizontal Difference Directional Examples Horizontal Difference Operator Vertical Difference Operator

Discrete Gradient Operators Pixels are samples on a discrete grid. Must estimate the gradient solely from these samples. STRATEGY: Build gradient estimation filter kernels and convolve them with the image. Two basic filter concepts First difference: Central difference:

Simple Filtering Example in 1-D Convolving with [ 5 5 5 8 20 25 25 22 12 4 3 3 ]   [ 0]

Simple Filtering Example in 1-D Convolving with [ 5 5 5 8 20 25 25 22 12 4 3 3 ]   [ 0 0]

Simple Filtering Example in 1-D Convolving with [ 5 5 5 8 20 25 25 22 12 4 3 3 ]   [ 0 0 3]

Simple Filtering Example in 1-D Convolving with [ 5 5 5 8 20 25 25 22 12 4 3 3 ]   produces: [ 0 0 3 12 5 0 -3 -13 -8 -1 0 ]

Gradient Estimation 1. Create orthogonal pair of filters, 2. Convolve image with each filter: 3. Estimate the gradient magnitude:

Roberts Operator Small kernel, relatively little computation First difference (diagonally) Very sensitive to noise Origin not at kernel center Somewhat anisotropic

Noise Noise is always a factor in images. Derivative operators are high-pass filters. High-pass filters boost noise! Effects of noise on edge detection: False edges Errors in edge position Key concept: Build filters to respond to edges and suppress noise.

Prewitt Operator Larger kernel, somewhat more computation Central difference, origin at center Smooths (averages) along edge, less sensitive to noise Somewhat anisotropic

Sobel Operator 3 x 3 kernel, same computation as Prewitt Central difference, origin at center Better smoothing along edge, even less sensitive to noise Still somewhat anisotropic

Discrete Operators Compared Original Roberts

Roberts Prewitt

Prewitt Sobel

T = 5 T = 10 Roberts T = 40 T = 40 T = 20

Continuous Laplacian This is a scalar. It’s also isotropic. Edge detection: Find all points for which No thinning is necessary. Tends to produce closed edge contours.

Discrete Laplacian Operators Origin at center Only one convolution needed, not two Can build larger kernels by sampling Laplacian of Gaussian

Laplacian of Gaussian (Marr-Hildreth Operator) Let: Then:

LoG Filter Impulse Response

LoG Filter Frequency Response

Laplacian of Gaussian Examples

LoG Properties One filter, one convolution needed Zero-crossings are very sensitive to noise (2nd deriv.) Bandpass filtering reduces noise effects Edge map can be produced for a given scale Scale-space or pyramid decomposition possible Found in biological vision!! Practical LoG Filters: Kernel at least 3 times width of main lobe, truncate Larger kernel  more computation

Summary Edges can be detected from the derivative: Extrema of gradient magnitude Zero-crossings of Laplacian Practical filter kernels; convolve with image Noise effects False edges Imprecise edge locations Correct filtering attempts to control noise Edge map is the goal

Questions?